How did the "Third World" develop in 1940-1975 in comparison to the Second and First Worlds?
During this time period, the Third World developed somewhat unevenly. Some countries developed quite a lot while others only developed a little. Where there was growth, it was generally faster than growth in either the Second or First Worlds.
The Third World was, of course, made up of the countries that had the least development to begin with. This meant that they had the most room to grow. Therefore, there were some countries that experienced very high rates of growth indeed. A good example of this is South Korea. This was a country that was devastated by having been colonized and then by war. Once it started to develop, it experienced rapid growth, with its GDP per capita roughly doubling between 1960 and 1975. However, there were countries, such as many African countries, that did not enjoy much growth at all. Because of this, it is hard to characterize the growth of the Third World as a whole.
The First World did grow during this time period, particularly after the end of WWII. However, these countries started from a much higher level and did not have as much room to grow. For example, both the UK and the US grew at about half the rate of South Korea (in terms of GDP per capita) during the 1960 to 1975 period. The Second World typically did not experience as much growth. Because these countries were communist, they did not have market economies to drive growth. This would haunt them after 1975 because they did not grow enough to keep their populaces happy.
Thus, the best way to answer this question is to say that growth in the Third World was uneven while the First World grew steadily, if not spectacularly. Meanwhile, the Second World did not experience as much growth because of its economic system.